Question: Multiply the following complex numbers: $({1-2i}) \cdot ({4})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1-2i}) \cdot ({4}) = $ $ ({1} \cdot {4}) + ({1} \cdot {0}i) + ({-2}i \cdot {4}) + ({-2}i \cdot {0}i) $ Then simplify the terms: $ (4) + (0i) + (-8i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 4 + (0 - 8)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 4 + (0 - 8)i - 0 $ The result is simplified: $ (4 - 0) + (-8i) = 4-8i $